[Stratoscope]

This reminds me of a math puzzle I read many years ago. It went something like this:

"Assume the Earth is a perfect sphere, and its circumference is 25,000 miles. You have a 25,000 mile long rope looped all the way around the Equator, so it is tight against the surface. Now you want to raise the rope one foot in the air, all the way around. How much more rope do you need?"

I thought about this and said, "You need a lot more rope! I don't know how much, but it will be a lot. It has to reach all the way around the Earth, only higher!"

Of course the real answer is "You only need about three more feet. To be specific, you need another 3.14159... feet."

That's all you need to raise a rope a foot in the air, all the way around the Earth.

[staticautomatic]

I had a science test in high school with a question that involved something to do with calculating the air pressure inside an airplane at some high altitude. I went up to to the teacher and said "is this a trick question? Airplanes are pressurized at that altitude" He looked around the room nervously and then told me to assume the airplane wasn't pressurized.

[Stratoscope]

Ah yes, the notorious spherical cow!

https://en.wikipedia.org/wiki/Spherical_cow

[Ono-Sendai]

circumference = 2 pi r, so increasing the radius by 1 foot will increase the circumference by 2 pi feet, not pi feet.

[Stratoscope]

Thank you! I had a feeling something must be off in my 50-year-old memory of this puzzle.

I'd better buy an extra 3-4 feet of rope before I try this experiment.

[Steve44]

A related one is to add a second section to the question asking how much extra rope would be needed to go round a tennis ball the same 1ft further out from the ball.

For someone who doesn’t know, or hasn’t calculated/thought about it that is pretty astounding.